(1) Field of the Invention
The present invention relates to a system and method for generating a free curved surface and specifically relates to a free curved surface generating system and a method which facilitates a correction of the free curved surface.
(2) Background of the Art
Various free curved surface generating systems have been proposed in which three-dimensional image information previously written into a memory is processed via transformation to construct a solid figure image which is to be three-dimensionally displayed on a raster scanned display screen of a display unit.
In such kinds of free curved surface generating systems, a plurality of cross sectioned curves, indicating the cross sectional shape at a plurality of arbitrary positions of the solid of the figure to be generated, are generated in an x-y coordinate system. These cross sectional curves are arranged at desired positions in an x-y-z coordinate system. Free surfaces are formed between these cross sectional curves through interpolations, and data representing the solid of the figure constituted by the free curved surfaces are prepared.
A multiple number of coordinate transformations for cross sectional curves are carried out between the x-y coordinate system and the x-y-z coordinate system and then the shapes of the cross sectional curves are corrected so as to generate a free curved surface of a desired shape.
However, at this time, rotations (angular quantities through which the cross sectional curves are rotated) and parallel translations for the cross sectional curves individually and repeatedly need to be set by a designer whenever the cross sectional curves are transformed from the x-y coordinate system into the x-y-z coordinate system and vice versa. Therefore, the correcting operations carried out by the designer, for correcting the cross sectional curves, become troublesome.
In addition, for example, through a technique disclosed in a Japanese Patent Application First Publication sho 62-226281 published on Oct. 5, 1987 the profile of the free surface is corrected in the x-y-z coordinate system and thereafter cross sectional curve(s) for the corrected part(s) need to be transformed into the x-y coordinate system in order to visually inspect the profile of the cross section. In this case, the designer similarly needs to set the rotations and parallel translations of the corrected cross sectional curves. Hence, as well as in this case, the designer's correcting operations for the free curved surface becomes complicated and troublesome.